The constant influence of passwords over all other methods of identity authentication is a key discomfiture to security examiners. Web technologies are gaining more and more fame day by day but the persistent survival and replication of password authentication schemes generate difficulties for end users. After such a long age, still discussions over substitute schemes have not yet produced an ultimate solution. The main aim of this paper is to compile a framework for the assessment of hash based password authentication schemes. We present a review of strong password authentication schemes and propose a suitable new hash chain based strong password authentication scheme that can fulfill highest possible level of desired criteria according to the framework.